Batch single reaction

The general stoichiometric relationships for a single reaction in a batch reactor are... 

Equilibrium Compositions for Single Reactions. We turn now to the problem of calculating the equilibrium composition for a single, homogeneous reaction. The most direct way of estimating equilibrium compositions is by simulating the reaction. Set the desired initial conditions and simulate an isothermal, constant-pressure, batch reaction. If the simulation is accurate, a real reaction could follow the same trajectory of composition versus time to approach equilibrium, but an accurate simulation is unnecessary. The solution can use the method of false transients. The rate equation must have a functional form consistent with the functional form of K,i,ermo> e.g., Equation (7.38). The time scale is unimportant and even the functional forms for the forward and reverse reactions have some latitude, as will be illustrated in the following example. 

Hence, both Cp and U can be evaluated for the physical and geometrical system under consideration instead of using literature correlations with an accuracy of 30 %. For a single reaction the rate of heat generation qp is the product of the reaction rate, the volume of the reaction mixture, and the heat of reaction, which for a batch apparatus can be written as ... 

Generally, the temperature changes with time or, equivalently, with distance from the reactor inlet (for flow reactors). This change is usually controlled well in reaction calorimeters but can become uncontrolled in other conventional laboratory flow or (semi)batch reactors. The balance equations of a batch reactor for a single reaction of a-th order kinetics are given by ... 

The next two steps after the development of a mathematical process model and before its implementation to "real life" applications, are to handle the numerical solution of the model s ode s and to estimate some unknown parameters. The computer program which handles the numerical solution of the present model has been written in a very general way. After inputing concentrations, flowrate data and reaction operating conditions, the user has the options to select from a variety of different modes of reactor operation (batch, semi-batch, single continuous, continuous train, CSTR-tube) or reactor startup conditions (seeded, unseeded, full or half-full of water or emulsion recipe and empty). Then, IMSL subroutine DCEAR handles the numerical integration of the ode s. Parameter estimation of the only two unknown parameters e and Dw has been described and is further discussed in (32). 

Single Reactions—For all reactions of orders above zero, tire CSTR gives a lower production rate than the batch, semi-batch, or kinetically equivalent plug-flow reactor. 

In this chapter we consider the performance of isothermal batch and continuous reactors with multiple reactions. Recall that for a single reaction the single differential equation describing the mass balance for batch or PETR was always separable and the algebraic equation for the CSTR was a simple polynomial. In contrast to single-reaction systems, the mathematics of solving for performance rapidly becomes so complex that analytical solutions are not possible. We will first consider simple multiple-reaction systems where analytical solutions are possible. Then we will discuss more complex systems where we can only obtain numerical solutions. 

For a single reaction in a nonisothermal batch reactor we can write the species and energy-balance equations... 

At the same time, as a chemist I was disappointed at the lack of serious chemistry and kinetics in reaction engineering texts. AU beat A B o death without much mention that irreversible isomerization reactions are very uncommon and never very interesting. Levenspiel and its progeny do not handle the series reactions A B C or parallel reactions A B, A —y C sufficiently to show students that these are really the prototypes of aU multiple reaction systems. It is typical to introduce rates and kinetics in a reaction engineering course with a section on analysis of data in which log-log and Anlienius plots are emphasized with the only purpose being the determination of rate expressions for single reactions from batch reactor data. It is typically assumed that ary chemistry and most kinetics come from previous physical chemistry courses. 

COMPARISON OF BATCH, TUBULAR AND STIRRED-TANK REACTORS FOR A SINGLE REACTION. REACTOR OUTPUT... 

Figu re 6.3 Batch reactor For a single reaction of the type A + B -> P, both reactants A and B are charged initially into the vessel. Therefore, temperature control is practically the only way to influence the reaction course. 

The fed-batch reactors considered in Sections 4.1, 4.2, and 4.6 all involved single reactions. The control problem was to prevent reaction temperature mnaways. In fed-batch... 

In the regime of slow single reactions semi-batch systems including valves will be adequate. 

Microreactors for long single reactions Semi-batch systems including valves... 

In batch reactors, for thermally simple types of reactions, that is, ones that can be attributed to a single reaction step, generally applicable to the propagation step of polymerization reactions, we can write the following thermal energy balance (6)... 

For a single reaction and known kinetics the balance for A, either Eqn. 7.1 or 7.3, can be integrated at a given temperature to yield a relation between the batch time and the degree of conversion ... 

If t is the time from the end of the batch process, the course of a single reaction is described by the equations (cf. Section 3.6)... 

Equation (7-54) allows calculation of the residence time required to achieve a given conversion or effluent composition. In the case of a network of reactions, knowing the reaction rates as a function of volumetric concentrations allows solution of the set of often nonlinear algebraic material balance equations using an implicit solver such as the multi variable Newton-Raphson method to determine the CSTR effluent concentration as a function of the residence time. As for batch reactors, for a single reaction all compositions can be expressed in terms of a component conversion or volumetric concentration, and Eq. (7-54) then becomes a single nonlinear algebraic equation solved by the Newton-Raphson method (for more details on this method see the relevant section this handbook). 

The following example concerning the rate of esterification of butanol and acetic acid in the liquid phase illustrates the design problem of predicting the time-conversion relationship for an isothermal, single-reaction, batch reactor. 

For constant-volume batch reactors with single reactions, and selecting the initial state as the reference state, the design equation, Eq. 6.2.1, reduces to... 

We continue the analysis of ideal, isothermal, constant-volume batch reactors with single reactions and consider now chemical reactions involving more than one reactant. Consider the general reaction form... 

We divide the chapter into two parts Part 1 Mote Balances in Terms of Conversion, and Part 2 Mole Balances in Terms of Concentration, C,. and Molar Flow Rates, F,." In Pan 1, we will concentrate on batch reactors, CSTRs, and PFRs where conversion is the preferred measure of a reaction s progress for single reactions. In Part 2. we will analyze membrane reactors, the startup of a CSTR. and semibatch reactors, which are most easily analyzed using concentration and molar How rates as the variables rather than conversion. We will again use mole balances in terms of these variables (Q. f,) for multiple reactors in Chapter 6. 

Here, a is a dummy variable of integration that will be replaced by the upper and lower limits after the integral is evaluated. The results are equivalent to those obtained earlier, for example. Equations 1.26 and 1.29 depending on the reaction order, and all the restrictive assumptions still apply a single reaction in a constant-volume, isothermal, perfectly mixed batch reactor. Note that Equation 1.33 becomes useless for the multiple reactions treated in Chapter 2. 

Formal verification that this result actually satisfies Equation 14.13 is an exercise in partial differentiation, but a physical interpretation will confirm its validity. Consider a small group of molecules that are in the reactor at position z at time t. They have been in the reactor for z/m seconds and entered at clock time t — z/u) when the inlet concentration was a n t — z/u). Their composition has subsequently evolved according to batch reaction kinetics. Equation 1.33 gives the time needed to go from an initial concentration to a current concentration when there is a single reaction in an ideal batch reactor. Equation 14.14 is just Equation 1.33 with different notation. 

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